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Prediction of the effective parameters of the nanofluids using the generalized stochastic perturbation method

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  • Kamiński, Marcin
  • Ossowski, Rafał Leszek

Abstract

The paper presents the results concerning a new problem of homogenization of the fluids filled with a random volume fraction of nanoparticles. We use a variety of probabilistic and statistical methods applied for numerical determination of the effective physical properties of different fluids filled with nanoparticles. The new probabilistic approach in the form of a higher order stochastic perturbation method is employed here, which is based on a higher order Taylor expansion of input random quantities and the resulting homogenized parameters using a general order series with random coefficients; it is contrasted with the Monte Carlo simulation and analytical symbolic integration. All computer methods are used to determine up to the fourth probabilistic moments and coefficients for effective specific heat, viscosity, heat conductivity and mass density for some nanofluids of modern technological importance. The volume fraction of the nanoparticles is treated in this study as the input Gaussian parameter truncated to the positive values and uniquely defined by the expectation, where its coefficient of variation is an additional parameter in our analysis. Computational experiments are performed here using computer algebra system MAPLE and they demonstrate a very good agreement of the probabilistic characteristics computed using analytical, perturbation and simulation methods.

Suggested Citation

  • Kamiński, Marcin & Ossowski, Rafał Leszek, 2014. "Prediction of the effective parameters of the nanofluids using the generalized stochastic perturbation method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 10-22.
  • Handle: RePEc:eee:phsmap:v:393:y:2014:i:c:p:10-22
    DOI: 10.1016/j.physa.2013.09.015
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    Cited by:

    1. Li, Zhixiong & Sheikholeslami, M. & Ayani, M. & Shamlooei, M. & Shafee, Ahmad & Waly, Mohamed Ibrahim & Tlili, I., 2019. "Acceleration of solidification process by means of nanoparticles in an energy storage enclosure using numerical approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 540-552.
    2. Jamei, Mehdi & Ahmadianfar, Iman, 2020. "A rigorous model for prediction of viscosity of oil-based hybrid nanofluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    3. Sheikholeslami, M. & Jafaryar, M. & Shafee, Ahmad & Li, Zhixiong, 2019. "Simulation of nanoparticles application for expediting melting of PCM inside a finned enclosure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 544-556.
    4. Sheikholeslami, M. & Keramati, Hadi & Shafee, Ahmad & Li, Zhixiong & Alawad, Omer A. & Tlili, I., 2019. "Nanofluid MHD forced convection heat transfer around the elliptic obstacle inside a permeable lid drive 3D enclosure considering lattice Boltzmann method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 87-104.
    5. Solangi, K.H. & Kazi, S.N. & Luhur, M.R. & Badarudin, A. & Amiri, A. & Sadri, Rad & Zubir, M.N.M. & Gharehkhani, Samira & Teng, K.H., 2015. "A comprehensive review of thermo-physical properties and convective heat transfer to nanofluids," Energy, Elsevier, vol. 89(C), pages 1065-1086.

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